Question: Determine the value of the following complex number power. Your answer will be plotted in orange. $ ({ e^{5\pi i / 12}}) ^ {9} $
Solution: Since $(a ^ b) ^ c = a ^ {b \cdot c}$ $ ({ e^{5\pi i / 12}}) ^ {9} = e ^ {9 \cdot (5\pi i / 12)} $ The angle of the result is $9 \cdot \frac{5}{12}\pi$ , which is $\frac{15}{4}\pi$ Our result is $ e^{7\pi i / 4}$.